Linear superposition time for variable-rate, variable-pressure production from a fractured tight gas well

Date

2020-05-01

Author

Gül Ertunç, Kıymet Gizem
Onur, Mustafa
Ozkan, Erdal

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Hydraulically fractured, tight gas wells produce under large pressure drawdowns, which may cause three-to ten-fold variations in the gas viscosity-compressibility product, particularly in the vicinity of the fracture, over the life of the production. Under such a large variation, the pseudo-pressure transformation cannot remove nonlinearity of the gas diffusion equation. The remaining nonlinearity makes the application of superposition principal questionable; specifically the linear superposition time based on linear flow, a dominant flow regime for hydraulically fractured tight gas reservoirs. Not accounting for the effect of large gas viscosity-compressibility product variations in pressure and rate transient analysis of fractured, tight gas well performances leads to misinterpretation of reservoir characteristics. In this paper, a perturbation-Green's function solution is developed for the nonlinear gas diffusion equation. Because each term in the perturbation solution represents the solution for a linearized problem, term-by-term application of the superposition principal is permitted. The semi-analytical nature of the solution also enables us to derive approximations for practical use. This paper explains the solution procedure, compares and verifies the solution with existing simulators presents variable-rate approximations in terms of new superposition time and discusses the results to provide guidelines for the analysis of fractured, tight gas well performances under large variations of viscosity and compressibility.

URI

https://hdl.handle.net/11511/117550

Collections

Department of Petroleum and Natural Gas Engineering, Article